We know humans never stay at a constant level of happiness from whatever we get. I am curious about how to answer this question: at what level of achievement, we will be able to reach the highest level of happiness.

So I propose the model with its assumptions to analyze the questions raised above.

Assumption I:

An individual’s happiness is proportionate to the gap between his achievement (what he has) and his expectation (what he wants to get), instead of the absolute level of his achievement. In another word, how much you own won’t determine how happy you are. However, how much more you gain than what you have expected will bring you a lot of happiness. Therefore, H (happiness) should be a monotonously increasing function of (A-E). Though I am aware that there are many other ways to describe the relationship, here I tentatively propose a simple linear model as below.( Eq.1) H = m * (A – E) + n
where m is called an emotion coefficient, and n is an emotion constant. In particular, m > 0, and n > 0.n indicates the happiness level when the person right achieves what he has expected. This model is illustrated in Figure 1 below.

Figure 1 Relationship between Happiness, Achievement and Expectation

Assumption II:

We speculate that people tend to expect more as they achievement rises. Therefore, I propose an exponential relationship between E (expectation) and A (achievement), though there could be other choices for modeling this too. This assumes that, when human achieve something, they would expect more on that base of their achievement. The formula to describe this assumption is as below.
(Eq.2) E = k * exp ( l * A )
where k is called ambition constant, and l is ambition coefficient. In particular, k > 0, and l > 0. It says, more ambitious persons have bigger k and l. k indicates the initial ambition level when his achievement is 0. This is demonstrated in Figure 2 below.

Therefore, for people with kl >= 1, since A*<=0 and the function is convex, their maximum happiness is reached at the time they haven’t achieved anything (A=0). For people with kl < 1, their maximum happiness is reached at some point of receiving achievements at certain level.

The indication here for people with greater ambition (kl>=1) is that, achieving more makes them less happy. This sounds striking!

This could also be a reminder for such “ambitious” people who want to get bigger happiness via making greater achievement. They’d better stay home doing nothing. Alternatively, they can change their personality first (change their k and l, but can this happen?), and then try making achievements to increase happiness.

Note: due to the simplicity, this model assumes the risk of being misleading…It is just for fun…

Written by Jianxi Luo, September 26th, 2009 at 12:31 pm, Posted in Philosophy

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[...] about life. If you like Math or solving complex equations, you may want to check out the simple model of happiness at IdeaSea.org. It’s a very interesting explanation and perspective Share and [...]

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This blog was started when I was a doctoral student at MIT (2006~2010), as a reservoir to store my original thoughts and ideas on life and anything, and a permanent place to share them to anyone that runs into this site. One's life is to end one day, but his ideas may remain forever. You can see that most of the "ideas" here are still those from my years as a doctoral student at MIT. Thanks to my supervisors and MIT for giving me the opportunity to think freely, deeply, and systematically, at the time. But note that, ideas here have nothing to do with my academic research. After my PhD at MIT and one year stint in New York City, now I am an assistant professor at Singapore University of Technology & Design. Please refer to this website or me properly when you quote or use the content and ideas originally from this website. Thanks.
Jianxi Luo